Uniform fuzzy relations and fuzzy functions

  • Authors:

  • Miroslav Ćirić;Jelena Ignjatović;Stojan Bogdanović

  • Affiliations:

  • Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 224, 18000 Niš, Serbia;Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 224, 18000 Niš, Serbia;Faculty of Economics, University of Niš, Trg Kralja Aleksandra 11, 18000 Niš, Serbia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2009

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Abstract

In this paper we introduce and study the concepts of a uniform fuzzy relation and a (partially) uniform F-function. We give various characterizations and constructions of uniform fuzzy relations and uniform F-functions, we show that the usual composition of fuzzy relations is not convenient for F-functions, so we introduce another kind of composition, and we establish a mutual correspondence between uniform F-functions and fuzzy equivalences. We also give some applications of uniform fuzzy relations in approximate reasoning, especially in fuzzy control, and we show that uniform fuzzy relations are closely related to the defuzzification problem.